Chops and Erosity - Mid Atlantic Madness

[muon2]

As I noted above the chop of Saratoga County in my map is right on the edge, very close to the point where the chop can be lost, with the Albany CD taking Hamilton County instead.

Granted in some cases the precinct lines do not fit, but it should be villages that are used (the precinct lines can be corrected). Even if the entirety of the territory is not covered in villages, the odd territory remaining would need to be cut reasonably to keep the erosity score down.

I asked you before to remind me what the penalty is for a subdivision chop, and again for a bridge chop. My impression in both cases is that it results in more erosity penalty points.

A bridge chop incurs a penalty if it causes the counties to be connected only by local roads and not be regional roads. Groups of regionally connected counties are called components and a plan gets an erosity point for each component in a district in excess of 1. Note that this definition also solves the nick cut problem when counties are otherwise locally connected.

In a macrochop the rule is clear - a subdivision chop gets treated just like a county chop. For other chops we've gone back and forth. It's clear we like chops to be made of whole subunits, at least that's what we are doing in upstate NY.  If so, then chopping a subunit should be counted as any other chop. Otherwise why bother keeping subunits whole in upstate. However, you have in the past desired a "one bite" rule which allows one subunit to be chopped as part of a chop of the unit containing it. If that's applied uniformly then a simple chop of a county can include one chopped subunit.

I understand about villages, but subunits have to cover all the population of a county. They can be a hybrid of different units, such as incorporated cities and remaining school districts as we did in WA. The key point is that no population in the county can be left out of the defined subunits. If villages leave population unassigned, what is the mechanism for assigning that remmant population?

[Torie]

As I noted above the chop of Saratoga County in my map is right on the edge, very close to the point where the chop can be lost, with the Albany CD taking Hamilton County instead.

Granted in some cases the precinct lines do not fit, but it should be villages that are used (the precinct lines can be corrected). Even if the entirety of the territory is not covered in villages, the odd territory remaining would need to be cut reasonably to keep the erosity score down.

I asked you before to remind me what the penalty is for a subdivision chop, and again for a bridge chop. My impression in both cases is that it results in more erosity penalty points.

A bridge chop incurs a penalty if it causes the counties to be connected only by local roads and not be regional roads. Groups of regionally connected counties are called components and a plan gets an erosity point for each component in a district in excess of 1. Note that this definition also solves the nick cut problem when counties are otherwise locally connected.

In a macrochop the rule is clear - a subdivision chop gets treated just like a county chop. For other chops we've gone back and forth. It's clear we like chops to be made of whole subunits, at least that's what we are doing in upstate NY.  If so, then chopping a subunit should be counted as any other chop. Otherwise why bother keeping subunits whole in upstate. However, you have in the past desired a "one bite" rule which allows one subunit to be chopped as part of a chop of the unit containing it. If that's applied uniformly then a simple chop of a county can include one chopped subunit.

I understand about villages, but subunits have to cover all the population of a county. They can be a hybrid of different units, such as incorporated cities and remaining school districts as we did in WA. The key point is that no population in the county can be left out of the defined subunits. If villages leave population unassigned, what is the mechanism for assigning that remmant population?

You have the same issue as between cities and unassigned territory. And villages are real. They are incorporated with real powers. They are not mere hamlet addresses, such as Stottville or Spencertown in Columbia County.

Regarding unassigned territory, if most is assigned, with just a few gaps, does it matter much? Just assign a penalty point for each village that appends it that is in a different CD.

Thanks for the other explanations. I prefer the one bite rule (it should not be the same as a county chop, which is far more important, as most would agree), but there should be a preference where there is no bite at all. I know you don't like preferences, but not having one, defies common sense.

Your bridge chop rule is way too weak for me. In most cases, it will be possible to avoid severing a state road. To not penalize a bridge chop at all where such severing is avoided, I think can lead to mischief, and allows to much discretion. I dissent.

[muon2]

As I noted above the chop of Saratoga County in my map is right on the edge, very close to the point where the chop can be lost, with the Albany CD taking Hamilton County instead.

Granted in some cases the precinct lines do not fit, but it should be villages that are used (the precinct lines can be corrected). Even if the entirety of the territory is not covered in villages, the odd territory remaining would need to be cut reasonably to keep the erosity score down.

I asked you before to remind me what the penalty is for a subdivision chop, and again for a bridge chop. My impression in both cases is that it results in more erosity penalty points.

A bridge chop incurs a penalty if it causes the counties to be connected only by local roads and not be regional roads. Groups of regionally connected counties are called components and a plan gets an erosity point for each component in a district in excess of 1. Note that this definition also solves the nick cut problem when counties are otherwise locally connected.

In a macrochop the rule is clear - a subdivision chop gets treated just like a county chop. For other chops we've gone back and forth. It's clear we like chops to be made of whole subunits, at least that's what we are doing in upstate NY.  If so, then chopping a subunit should be counted as any other chop. Otherwise why bother keeping subunits whole in upstate. However, you have in the past desired a "one bite" rule which allows one subunit to be chopped as part of a chop of the unit containing it. If that's applied uniformly then a simple chop of a county can include one chopped subunit.

I understand about villages, but subunits have to cover all the population of a county. They can be a hybrid of different units, such as incorporated cities and remaining school districts as we did in WA. The key point is that no population in the county can be left out of the defined subunits. If villages leave population unassigned, what is the mechanism for assigning that remmant population?

You have the same issue as between cities and unassigned territory. And villages are real. They are incorporated with real powers. They are not mere hamlet addresses, such as Stottville or Spencertown in Columbia County.

Regarding unassigned territory, if most is assigned, with just a few gaps, does it matter much? Just assign a penalty point for each village that appends it that is in a different CD.

Thanks for the other explanations. I prefer the one bite rule (it should not be the same as a county chop, which is far more important, as most would agree), but there should be a preference where there is no bite at all. I know you don't like preferences, but not having one, defies common sense.

Your bridge chop rule is way too weak for me. In most cases, it will be possible to avoid severing a state road. To not penalize a bridge chop at all where such severing is avoided, I think can lead to mischief, and allows to much discretion. I dissent.

I went through a lot of examples that had bridge chops and why people put them in. I looked at my proposed rule from the purely theoretical, too. I'm actually quite confident that this rule causes no more mischief than the basic chop rule. I'm open to a case that causes such mischief that it could be rethought. Show me the basis for your dissent.

Since you prefer the one bite rule, but not at the level of counties, does that mean you only want it for sub-subdivisions? If so, and NYC is divided up into the neighborhoods we discussed, then those are only first level subdivisions and the one bit rule wouldn't apply. Yet predefined neighborhoods in Chicago (77 community areas tied to the Census) would be second level and one-bite would apply. Am I getting any of this right?

I'm completely blank on your suggestion for unassigned territory. Every census block must be assigned to a subdivision before maps are drawn other wise the scoring becomes arbitrary and algorithms fail. If Nassau's villages are incorporated like cities can the the remaining area be fragments of the unincorporated town? I'm thinking of the pieces of townships left in Hamilton county OH between Cincinnati. It doesn't help that some of the places in a town in Nassau are actually villages (eg Atlantic Beach) and others are Census Designated Places (eg East Atlantic Beach) and they are all sub-subdivisions of the county as opposed to OH where they are just county subdivisions.

Edit: Upon investigation I learned a little more about places in Nassau. There are five county subdivisions. Glen Cove and Long Beach are cities. Hempstead town is totally filled by villages and CDPs, so there is no issue with remnant population. North Hempstead and Oyster Bay towns do have remnant 2010 populations of 571 and 405 respectively. I know these are small, but they still have to be definitively assigned either to a place or as their own fragments prior to mapping.

Edit 2: I checked Suffolk as well. There are 12 county subdivisions, but only two towns that have any 2010 population not in a village or CDP: Brookhaven town has 18 and Huntington town has 30. Of course the algorithms still need them assigned to some sub-subunit despite their small size.

[jimrtex]

As I noted above the chop of Saratoga County in my map is right on the edge, very close to the point where the chop can be lost, with the Albany CD taking Hamilton County instead.

Granted in some cases the precinct lines do not fit, but it should be villages that are used (the precinct lines can be corrected). Even if the entirety of the territory is not covered in villages, the odd territory remaining would need to be cut reasonably to keep the erosity score down.

I asked you before to remind me what the penalty is for a subdivision chop, and again for a bridge chop. My impression in both cases is that it results in more erosity penalty points.

A bridge chop incurs a penalty if it causes the counties to be connected only by local roads and not be regional roads. Groups of regionally connected counties are called components and a plan gets an erosity point for each component in a district in excess of 1. Note that this definition also solves the nick cut problem when counties are otherwise locally connected.

In a macrochop the rule is clear - a subdivision chop gets treated just like a county chop. For other chops we've gone back and forth. It's clear we like chops to be made of whole subunits, at least that's what we are doing in upstate NY.  If so, then chopping a subunit should be counted as any other chop. Otherwise why bother keeping subunits whole in upstate. However, you have in the past desired a "one bite" rule which allows one subunit to be chopped as part of a chop of the unit containing it. If that's applied uniformly then a simple chop of a county can include one chopped subunit.

I understand about villages, but subunits have to cover all the population of a county. They can be a hybrid of different units, such as incorporated cities and remaining school districts as we did in WA. The key point is that no population in the county can be left out of the defined subunits. If villages leave population unassigned, what is the mechanism for assigning that remmant population?

You have the same issue as between cities and unassigned territory. And villages are real. They are incorporated with real powers. They are not mere hamlet addresses, such as Stottville or Spencertown in Columbia County.

Regarding unassigned territory, if most is assigned, with just a few gaps, does it matter much? Just assign a penalty point for each village that appends it that is in a different CD.

Thanks for the other explanations. I prefer the one bite rule (it should not be the same as a county chop, which is far more important, as most would agree), but there should be a preference where there is no bite at all. I know you don't like preferences, but not having one, defies common sense.

Your bridge chop rule is way too weak for me. In most cases, it will be possible to avoid severing a state road. To not penalize a bridge chop at all where such severing is avoided, I think can lead to mischief, and allows to much discretion. I dissent.

I went through a lot of examples that had bridge chops and why people put them in. I looked at my proposed rule from the purely theoretical, too. I'm actually quite confident that this rule causes no more mischief than the basic chop rule. I'm open to a case that causes such mischief that it could be rethought. Show me the basis for your dissent.

Since you prefer the one bite rule, but not at the level of counties, does that mean you only want it for sub-subdivisions? If so, and NYC is divided up into the neighborhoods we discussed, then those are only first level subdivisions and the one bit rule wouldn't apply. Yet predefined neighborhoods in Chicago (77 community areas tied to the Census) would be second level and one-bite would apply. Am I getting any of this right?

I'm completely blank on your suggestion for unassigned territory. Every census block must be assigned to a subdivision before maps are drawn other wise the scoring becomes arbitrary and algorithms fail. If Nassau's villages are incorporated like cities can the the remaining area be fragments of the unincorporated town? I'm thinking of the pieces of townships left in Hamilton county OH between Cincinnati. It doesn't help that some of the places in a town in Nassau are actually villages (eg Atlantic Beach) and others are Census Designated Places (eg East Atlantic Beach) and they are all sub-subdivisions of the county as opposed to OH where they are just county subdivisions.

Edit: Upon investigation I learned a little more about places in Nassau. There are five county subdivisions. Glen Cove and Long Beach are cities. Hempstead town is totally filled by villages and CDPs, so there is no issue with remnant population. North Hempstead and Oyster Bay towns do have remnant 2010 populations of 571 and 405 respectively. I know these are small, but they still have to be definitively assigned either to a place or as their own fragments prior to mapping.

Edit 2: I checked Suffolk as well. There are 12 county subdivisions, but only two towns that have any 2010 population not in a village or CDP: Brookhaven town has 18 and Huntington town has 30. Of course the algorithms still need them assigned to some sub-subunit despite their small size.

Villages in New York are not independent of towns, and may cross town and even county boundaries.

Cities in New York are not incorporated in the sense found elsewhere, but are chartered by the state legislature, and are treated as town equivalents for purposes of subdivision of counties.

Nonetheless, it is reasonable to base 3rd-level divisions in Nassau, Suffolk, Westchester, and Rockland on villages, at least for congressional district sized units. For county legislatures, towns may be ignored.

[jimrtex]

These are 5 county-level maps.

Jimrtex 19.0% cumulative deviation (this treats the two westernmost districts as one district, and disregards the Long Island and Staten Island districts). Interior perimeters 949 miles, and stranded persons: 87,747 persons (11.4%) to be shifted to bring the map into perfect equality.



Torie: 21.6%, 999 miles, 82,748 persons (10.8%)



Torie (modified by switching Cortland and Hamilton): 13.6%, 1077 miles, and 100,724 persons (13.1%) (though district deviations are decreased, an regional bias is introduced which requires some double shifts to eliminate).



Muon2: 14.0%, 1049 miles, 56,259 persons (7.3%)



Muon2 (modified by switching Seneca) 8.8%, 1058 miles, 35,874 persons (4.7%)



*****

Even if the boundaries are later fudged to comply with presumptive SCOTUS dictates, isn't this as much simpler and transparent way to evaluate maps.

[muon2]

Should the percentages add up to 0? Ie, the percentage are measured as a fraction of a quota, which is how we measured multi-district regions in the past.

It looks like these percentages are measured as a fraction of whole number of districts. At one point we thought that it might make sense to constrain the size of multi-district regions by something like the square root of the number of districts times the deviation. The idea being that it gets hard to follow subunits and maintain reasonable deviations when the multi-district region has itself a large deviation.

[muon2]

Here's hwo I would analyze the maps. I'm only going to consider the upstate CDs, and I'll treat the two Buffalo CDs as a single whole county region of size 2 and ignore internal chops. The number of chops are based on the fewest county divisions needed to bring populations to the level of minor variations cited in Tennant. Regional erosity uses this map of regional connections and counts the number of cut links. I ignore the ability of well-designed chops to reduce erosity.

These are 5 county-level maps.

Jimrtex 19.2% cumulative deviation (this treats the two westernmost districts as one district, and disregards the Long Island and Staten Island districts). Interior perimeters 1898 miles, and stranded persons: 87,747 persons to be shifted to bring the map into perfect equality.

Chops 5, Erosity 40

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Chops 5, Erosity 44

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Chops 6, Erosity 45

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Chops 3, Erosity 44

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Chops 3, Erosity 45

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Perimeter measurements are fine to a point, but they have known shortcomings. They overcount perimeters due to natural geography like rivers and mountains. For example Herkimer has a long perimeter up north that encloses little population and has no impact on erosity. Perimeters also undercount effects in urban areas since they aren't scalable to districts that pack in a city.

[jimrtex]

Should the percentages add up to 0? Ie, the percentage are measured as a fraction of a quota, which is how we measured multi-district regions in the past.

It looks like these percentages are measured as a fraction of whole number of districts. At one point we thought that it might make sense to constrain the size of multi-district regions by something like the square root of the number of districts times the deviation. The idea being that it gets hard to follow subunits and maintain reasonable deviations when the multi-district region has itself a large deviation.

The percentages on the map are deviation per district.

My New York-Bronx-Westchester-etc. region, has a a population of 5.936 quotas for 6 districts, or 0.989 per district. The map shows a deviation of -1.1% per district.

But in calculating the total deviation I used the combined deviation of -6.4%. What we are trying to calculate is the number of persons that have to be moved into or out of regions to bring them into total equality. For this purpose, I treated the Buffalo and Niagara Frontier regions as a single region having a deficit -0.2%. I also excluded the Long Island and Staten Island regions since they are the same for all the maps, and have a total magnitude extremely close to 11 quotas.

This percentage assumes that we can move people in and out without shifting boundaries. But we have to move people between adjacent districts. If districts with a surplus were adjacent to districts with a deficit, we can simply move people from the surplus regions to the deficit regions. The number of people moved can be as small as half the total deviation. That is, to equalize a region with a 3% surplus  with a region with a 3% deficit, we only need to shift population equivalent to 3% of a quota. Moving 3% reduces both the surplus and deficit by 3%.

But we might have to move people from a region with a surplus into a region with a deficit, and then on to another region with a bias. This can indicate a regional bias. This be seen most clearly with Torie's plan and the version that I modified by shifting Cortland. This reduces the total deviation, but increases the number of persons that have to be moved.

His plan was designed to reduce the amount of correction needed to approach equality, while the modified plan provides better equality among whole county regions.

To calculate the number of people that need to be shifted to achieve total equality, begin with a network where each node represents a region, and the links represent adjacent regions (here adjacency takes into account non-traversable boundaries such that the regions on either side are not considered to be adjacent).

We find a subnet that has exactly N-1 links, where N is the number of nodes, and there are no loops and would require the minimum number of persons shifted to reach full equality.

The amount shown does not include the shift between the Buffalo and Niagara Frontier region, but it does include a small shift from the Southern Tier-Finger Lakes region to the Niagara Region. It also does not include the shifts among the Long Island and State Island regions, or the tiny amount from Manhattan to the south. It does include a consequent adjustment in the upstate region.

*** Note I recalculated the total deviation using my spreadsheet. I also expressed the total shift amount as a percentage of a quota. And I halved the perimeter. I had measured the perimeter of each region and then summed them. This in effect doubles the length.

[jimrtex]

Here's hwo I would analyze the maps. I'm only going to consider the upstate CDs, and I'll treat the two Buffalo CDs as a single whole county region of size 2 and ignore internal chops. The number of chops are based on the fewest county divisions needed to bring populations to the level of minor variations cited in Tennant. Regional erosity uses this map of regional connections and counts the number of cut links. I ignore the ability of well-designed chops to reduce erosity.

These are 5 county-level maps.

Jimrtex 19.2% cumulative deviation (this treats the two westernmost districts as one district, and disregards the Long Island and Staten Island districts). Interior perimeters 1898 miles, and stranded persons: 87,747 persons to be shifted to bring the map into perfect equality.

Chops 5, Erosity 40

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Chops 5, Erosity 44

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Chops 6, Erosity 45

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Chops 3, Erosity 44

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Chops 3, Erosity 45

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Perimeter measurements are fine to a point, but they have known shortcomings. They overcount perimeters due to natural geography like rivers and mountains. For example Herkimer has a long perimeter up north that encloses little population and has no impact on erosity. Perimeters also undercount effects in urban areas since they aren't scalable to districts that pack in a city.

I used the straight-line distance measured from intersection to intersection. While there is some additional erosity caused by Herkimer in your and Torie's map it does not account for all the differences.  My Albany and Syracuse districts are more compact, as is the Finger Lakes-Southern Tier district because it is more square.

It is very hard to count erosity, and the rules for treating counties as being connected is close to capricious. New York in the past has had districts connecting Schoharie and Greene; Madison and Oswego; Hamilton and St. Lawrence; Herkimer and Lewis; Herkimer and St.Lawrence; and Allegany and Livingston.

Even including a connection between Seneca and Yates across Seneca Lake should be acceptable at the scale of congressional districts. The route from Waterloo to Penn Yan avoids the center of Ontario County.

Does the erosity measure scale within cities, and does it matter if it does or not? If a better division of Queen can be devised, should it matter to the upstate districts?

[muon2]

Does the erosity measure scale within cities, and does it matter if it does or not? If a better division of Queen can be devised, should it matter to the upstate districts?

I don't know about Queens but I gave this a close look when considering plans for WA and MI. Without scaling, gerrymandered divisions in and around Seattle or Detroit can get lost in the larger shapes of districts that extend out from the city and suburbs. Clever gerrymanders shouldn't be protected just because they are hidden in the high-density areas of a state. The exact definition of a macrochop as a percentage may be arbitrary but it is at about the right point to create a natural scaling.

[Torie]

Does the erosity measure scale within cities, and does it matter if it does or not? If a better division of Queen can be devised, should it matter to the upstate districts?

I don't know about Queens but I gave this a close look when considering plans for WA and MI. Without scaling, gerrymandered divisions in and around Seattle or Detroit can get lost in the larger shapes of districts that extend out from the city and suburbs. Clever gerrymanders shouldn't be protected just because they are hidden in the high-density areas of a state. The exact definition of a macrochop as a percentage may be arbitrary but it is at about the right point to create a natural scaling.

Macro-chops in highly populated counties, and the configuration of lines that define such chops, is where the bulk of the action as to gerrymanders occurs. If that is not tightened up, so that partisan numbers have little or no traction subject to the VRA as to where the macro-chop lines lie, the Muon2 rules are rendered largely toothless, and the exercise becomes largely a waste of time. Moving rural counties around, given the partisan divide these days, has a very minor impact in most places.